The theory of meaningful mathematics instruction based on the ontological-semiotic model of mathematical cognition called Theory of semiotics functions (TSF) provides a unified framework for studying the various forms of mathematical knowledge and their interactions within didactics systems (Godino, 2003).

We present a development of this theory consists in the decomposition of an object, in our model, the definition of limit of a function according to Weierstrass – as shown in middle school texts-, in units to identify entities – ostensive (notations), extensive (situation-problems), intensive (ideas, abstractions) and actuative entities (subject’s actions) and establishing semiotics functions for the understanding of the concepts: variations, intervals, neighborhood, convergence, point accumulation, absolute value, epsilon-delta definition; in the process of teaching and learning in an educational institutional implementing a digital technology environment (CAS -graphing calculator advanced voyage 200-).

Keywords

Primary entities, semiotics functions, digital technology environment, instruments of semiotic mediation(CAS), definition of limit of a function according to Weierstrass.